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A polynomial is really an algebraic expression that consists of two or more monomials. A monomial is a number, a variable, or a product of a number with non-negative exponents. Some examples of polynomials are:

2x+3y-1;3bc+7cd-y;7mny-my+n

To be exact, polynomials is any expression with the lowest power of unknown as 0 or more. 6z+5, 5x4+9x-1 are some examples of polynomials. However, if the unknown is in the denominator, it is not a polynomial. Also, if the expression has a negative power like 3-2, it will become a fraction when you remove the negative sign (3-2 = 1/32).-42 is a polynomial because it is also -42x0 except that people do not need to write the x0 since x0 = 1 and when you multiply -42x0, it still ends up becoming -42.

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when the co-efficient of variable in each term is a real number and the exponent of variable in each term is a whole number.

A polynomial can have constants (like 3, -20) variables (like x and y) exponents (like the 2 in y2) that can be combined using addition, subtraction, multiplication and division.It is important to keep in mind that except division by a variable (so something like 2/x).

Also, polynomials of a variable are easy to graph, as they have smooth and continuous lines.

Q: When is an algebraic expression considered as polynomial?

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A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. An algebraic expression is an expression with a variable in it, and a polynomial is an expression with multiple terms with variables in it.

Not really.For example: x can be considered and algebraic expression by itself, however it is only a single variable, so by definition it is not a polynomial expression (multiple-number expression).

if it has parentheses

monomial binomial trinomial polynomial

A polynomial is one possible answer.

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A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. In another polynomial is a subset of algebraic expression.

A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. An algebraic expression is an expression with a variable in it, and a polynomial is an expression with multiple terms with variables in it.

Not really.For example: x can be considered and algebraic expression by itself, however it is only a single variable, so by definition it is not a polynomial expression (multiple-number expression).

An expression is non polynomial if it has : negative exponent fractional exponent variable exponent in the radicand

A polynomial is a type of algebraic expression. They differ in the number of terms that contain variables. An algebraic expression has at least 1 variable, while a polynomial has multiple terms with variables in it.

Yes.

Yes

if it has parentheses

Yes

It is an algebraic factor.

monomial binomial trinomial polynomial

No. A matrix polynomial is an algebraic expression in which the variable is a matrix. A polynomial matrix is a matrix in which each element is a polynomial.